First, square each of the scores. {Entrance exam narrative} Bob’s score on this exam was 130. It is often safe to assume that our DVs are normally distributed in the general population • Oftentimes, normal distribution of the DV is an assumption, or rule, of our statistical tests 2. Normal Distribution & Z-scores This video shows how to calculate "inside areas" and "areas in the extreme" in a normal distribution using Z-scores. z Scores (also known as a standard scores) a. Area from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals). raw scores, in terms of normal distribution, inferential stats. A z-score is measured in units of the standard deviation. Make up your own numbers and use the web page to verify your computation. The Z-score value is the distance between the raw score or an individual member to the population mean in terms of Standard Deviations. NORMSDIST(z) Z is the value for which you want the distribution. This standardized scoring system has a midpoint of 5. The calculator reports that the population mean is 112. * Standardization is a simple linear transformation of raw scores, * so that the new distribution will have a mean of 1 and a. For a normal distribution, we define the z-score of a score as the number of standard deviations below or above the population mean a raw score is. 5 (Ross' foot length is 1. Standard Normal Distribution Problem and Solution. the newest data on GRE percentiles 2017. Z-Scores and the Normal Distribution. This section shows you how to find the z-score for a critical value in a left tail. the newest data on GRE percentiles 2017. 3372 area less than 70!0. Now, to be consistant, I used the same formula to convert our other raw score of 16. In this module, you are shown how to estimate the probability of getting a certain z-score value equal to or higher than the one that is observed. That is, the likelihood of observing z-scores of certain magnitudes can be read directly from Table D. 35) or use the Z-Score to Percentile Calculator (choose 1-sided) and get the percentages : 91% Verbal and 77% Quantitative. Confidence Intervals about µ, Known 28. This page includes the documentation of the SOCR Power Analysis Java applet. Derived Scores Quiz. The calculator allows area look up with out the use of tables or charts. In a normal distribution of scores, four participants obtained the following deviation scores: +1, -2, +5, and -10. 94 in the middle of the normal distribution curve. the sample means will have a normal distribution and standard deviation. Test the claim that the mean SAT score for Stevens High graduates is the same as the national average. If a normally distributed group of test scores has a mean of 70 and a standard deviation of 12, then what is the percentage of scores that will fall below 50? The random variable [math]X[/math] is [math]\text{N}(70\text{,}\space144)[/math] because. Assuming the test scores range from 0 to 100, you can define score bands like 10,20,30,40,50,60,70,80,90,100. , a standard normal score), given an unstandardized raw value, the population mean, and the standard deviation of the population to which the unstandardized value belongs. A normal distribution of scores has a standard deviation of 10. The z score is the numerical value which represents how many standard deviations a score is above the mean. CH6: The Normal Distribution Santorico - Page 196 Section 6-2: Applications of the Normal Distribution Finding Probabilities for Normal Distributions To find probabilities for any normal distribution with mean V P and standard deviation , we simply transform the values on the original scale (call these x, x 1, or x 2) using the formula z. The calculator will generate a step by step explanation along with the graphic representation of the area you want to find and standard normal tables you need to use. 3 ----- Z Scores: Red Blood Cell Count. Jennifer is taller than 85% of the population of U. from z-score we can calculate X =(s)(z)+X the online-app shows that for a standard normal, P 70 =0. If a researcher can assume that a given empirical distribution approximates the normal distribution, then he or she can assume that the data's z-scores approximate the z-scores of the normal distribution as well. Referring back to the normal curve, about 98% of the area of the curve would beto the left of this score and about 2% would be to the right. Pam’s score is 1800 1500 300 = 1 standard deviation above the mean. Other Relative Scores. Then, subtract that grade from 100. f of the standard normal distribution table", finds a probability valuse as close to 0. Normal Distribution When we can calculate probabilities for anypoint on the curve, our results will raw scores to standardized scores (a. When dealing with applications using the normal distribution, standardized the random variable to a standard normal random variable. While they are relatively simple to calculate by hand, R makes these operations extremely easy thanks to the scale() function. That is: (15 - 14) / 2 = 0. Use this applet to answer all questions which specify a range of raw or z-scores and ask for the probability. 4298249 to 211. A normal distribution has a mean of 50 and a standard deviation of 5. Excel vs SPSS - calculate Z Score and probability. 05, the Normal tables give the corresponding z-score as -1. 05) print(z) [1. How do I Convert a Z Score to Percentile? Use a calculator, like the one below, or use a table (see instructions further down) and calculate the percentile by hand. For example, if you scored in the 85th percentile, you scored higher than 85 percent of test takers. Also, make use of the example given below to understand the manual calculation steps. You would need to use the mean and the standard deviation and the z-score of 1. How to calculate a z-score? A z-score represents probability of a particular measure occurring. Z score of an observation is the number of standard deviations it falls above or below the mean. calculate the empirical rule). MedFriendly ® Standard Score to Percentile Conversion. We could use a table of z-scores, and we would find that the area under a normal curve with z-scores less than a 2 is 97. Tables of Normal Distribution • Predictions are made about ND populations by using Standard Table - Appendix in many books (-3 < Z < 3, 0. 6 Finding Probability under the Normal Curve 84 step-by-step illustration: finding the probability under the normal curve 84 5. (a) Find the standard clev'latlon of the normal distribution (4) (b) Find the probability that a viS1t lasts less than 25 mrnutes. How to find and interpret the z-score The z-score is a way of counting the number of standard deviations between a given data value and the mean of the data set. Z-scores tell us how many standard deviations a given "raw" score is from the mean. As the data size increases, distribution tends to be Z distribution. For each of the following heights, calculate the z-score and interpret it using complete sentences. Calculate new X values for raw scores of X = 64 and X = 43 o What proportion of a normal distribution corresponds to z-scores within 1. Examining the raw data is an essential first step before proceeding to statistical analysis. This is represented by the area. 4 and observing the coresponding area of. Finally, add that number to every student's grade. Applications of the Normal Distribution. For norm referenced scores such as t-scores, presumably you would need access to norm tables supplied in the test manual. In this case of t-scores, you would convert raw scores to z-scores and then multiply by 10 and then add 50. a measure of how many standard. Excel has some very useful functions for finding areas under the normal distribution. Using T Score to Calculate PSLE Aggregate Score Let’s now take a look at Li Ting’s total performance The cohort’s average and standard deviation plays a big part in Li Ting’s score. Possible scores are 590, 600, 610, etc. In this table are a bunch of z-scores and proportions for the Standard Normal Distribution (which is the z-score standarized Normal distribution). We can get a reasonable prior distribution by taking the distribution of scaled scores, mapping them back to raw scores, and converting raw scores to percentages. The points on a standard normal distribution, which is a bell curve that peaks at zero and has a standard deviation of one, correspond to z scores. However, once you calculate the test statistic, Excel can get the critical values and the P-values needed to complete the test. a) What is the standardized score of a student with a raw score of 87?. raw scores, in terms of normal distribution, inferential stats. How to calculate Z-Scores. Using the following transformation, a normal distribution of variable X. Under certain situations, statistical estimators converge to a normal distribution as outlined by the Central limit theorem. The mean of the sampling distribution (𝜇𝑋 ) always equals the mean of the raw score distribution from which we sampled (𝜇𝑋) 3. Example: In a distribution of scores of a doss Pinky’s percentile rank in statistics is 65. HYPOTHESIS TESTING: TWO MEANS, PAIRED DATA, TWO PROPORTIONS Example 10. The standard score (more commonly referred to as a z-score) is a very useful statistic because it (a) allows us to calculate the probability of a score occurring within our normal distribution and (b) enables us to compare two scores that are from different normal distributions. This identifies the probability of seeing that raw score within a standard normal distribution, expressed as the percentage of the normal distribution under that mark. from z-score we can calculate X =(s)(z)+X the online-app shows that for a standard normal, P 70 =0. In this lesson, we will look at the formula for the z-score, how to calculate it, and a little more closely at this idea of counting standard deviations. Z-Scores, Proportions, and Percentiles 1. Test your self to see if you can do this. In statistical data analysis, it is also called standard score, z value, standardized score and normal score. Z-scores review If you're seeing this message, it. Frequency Distribution BY: M. These are called standardized scores, or Z scores. Example 1: What proportion of test takers earn a score between 650 and 700? Solution: This is a calculation for individuals: μ = 500, σ = 100. Normal Probability Distribution Graph Interactive. Normal Distribution. These scores can be used to produce normal probability plots and various tests. 7, what is your percentile score? Solution: To figure out what percentile this score is in, we need to find the probability of getting a lower score, and then multiply by 100. Whoops! There was a problem previewing Continuous Probability Distribution Wokshop. Finding Areas under the Standard Normal Curve 23. 35) or use the Z-Score to Percentile Calculator (choose 1-sided) and get the percentages : 91% Verbal and 77% Quantitative. The answer is the standard-normal distribution. This calculator will do all the hard work for you. That is, the likelihood of observing z-scores of certain magnitudes can be read directly from Table D. Recommended Articles. Question: Basic Computation: Z Score And Raw Score A Normal Distribution Has = 30 And = 5. That calculator only works for a normal distribution, and I'm sure USMLE and COMLEX scores don't follow a normal distribution. Statistics Forum. by Winters, R. Then, we plug the known inputs (cumulative probability, standard deviation, sample mean, and degrees of freedom) into the calculator and hit the Calculate button. # The proportion of raw scores that fall above 90 is: 1-pnorm(90,mu,sigma) [1] 0. 2) However, a Standard Score will follow a normal distribution, also known as bell curve or Gaussian distribution. Use the table (Table V) to find the area under the standard normal distribution. = Number such that the area under the standard normal curve falling between z c and is equal to c. The functions used to get critical values and P-values are demonstrated here. Calculate the z score corresponding to x value of 40. Z scores are defined for distributions of any shape, but only when the distribution is normal can we use Z scores to calculate percentiles. Define the random variable. Returns the standard normal cumulative distribution function. There are the diverse application of z-score across fields if applied properly. You have a z-score of -. However, the sampling distribution of x is not as spread out as the population distribution. Calculate Raw Score from Z Score: Make use of this online z score to raw score calculator to conveniently find the raw score based on the z score. Thus, regardless of the details of the problem, we can calculate probabilities for any normal distribution using the standardized distribution. Finding a z score involves performing a two-part calculation using three figures. Know how to solve problems if we assume a normal distribution. Discussions of fair grading practice tend to focus on: grading methodology and individual assignments (i. Z-score Calculator. The sten scoring system is normally distributed and then divided into ten parts by letting 0. Page 1 of 4 Updated 27-Aug-19. The standard normal random variable is usually denoted by Z and this Z is the same as the Z-score. b) between 7 and 12 months. this can be seen in the following z-score calculator output. Parents struggle to understand how, when a paper may have 80 questions on it, the final score they are given can be a figure of, say, 130. These are called standardized scores, or Z scores. Normal distribution and Z scores: This 3-part diagram shows the percent of a normal distribution that lies between 1, 2, and 3 standard deviations from the mean: between -1 and 1 you can find approximately 68%; between -2 and 2 is approximately 95%; and between -3 and 3 is approximately 99. Once you do that, you can learn things about the population—and you can create some cool-looking graphs! How to Identify the Distribution of Your Data. Find the z-scores corresponding to each of the following values: a) A score that is 20 points above the mean. How to calculate a Z-score, and how to find the raw score (X) when you have a Z-score. Even though there are lots of steps to this method from start to finish, it is a fairly simple calculation. From the probability of a standard normal distribution one can find the associate z value or x value for the normal random variable. org) Comparing with z-scores. Standard normal failure distribution. Z score ranges from -3 to 3, while the T score ranges from 20 to 80. Review of Z Scores. Normal Distribution, “p” Value and Confidence Intervals NJ Gogtay, SP Deshpande, UM Thatte Dept. If your z-score is 2. The mean of the sampling distribution (𝜇𝑋 ) always equals the mean of the raw score distribution from which we sampled (𝜇𝑋) 3. NCE scores have a. Description: A WeBWorK problem that asks students to find z-scores given the area under the normal curve. I am reviewing process control charts for customers and have a problem with test of normality. PROPERTIES OF THE STANDARD NORMAL DISTRIBUTION 1. You can find normal probabilities using Minitab, Excel, and the TI-83. This means that one standard deviation of the raw score, no matter what the raw value is, always converts into 1 z score unit. I have a 1 Dimentional array and I can compute the "mean" and "standard deviation" of this sample and plot the "Normal distribution" but I have a problems: I want to plot the data and Normal distribution in the same figure like below : I dont know how to plot both the "DATA" and the "Normal Distribution". Thus, the shape of the distribution of z scores is identical to the distribution of raw scores. The (colored) graph can have any mean, and any standard deviation. A popular normal distribution problem involves finding percentiles for X. 5 Standard Scores and the Normal Curve 82 5. The standard deviation of any SND always = 1. See Adding Info to Lists for further help on entering your data. THE NORMAL CURVE AND "Z" SCORES: The Normal Curve: The "Normal" curve is a mathematical abstraction which conveniently describes many distributions of data in the natural and biological sciences. We can get a reasonable prior distribution by taking the distribution of scaled scores, mapping them back to raw scores, and converting raw scores to percentages. +3 standard deviations from the mean 3. For example, you may wish to determine if there is a statistically significant difference between anxiety levels before and after a proposed treatment strategy. Raw Scores are simply the average of all responses. Especially if you have limited experience with standardized testing, the speech-language pathologist's explanations may sound like complete gibberish. By converting normally distributed scores (either the observed data or the theoretical sampling distribution of the mean) into z scores, we can ascertain the probabilities of obtaining specific ranges of scores using either a table for the standard normal distribution (i. Ross: z-score = (13. Standard Normal Distribution Z-Score Calculator This calculator will tell you the normal distribution Z-score associated with a given cumulative probability level. To find the mean and higher moments of the lognormal distribution, we once again rely on basic information about normal distribution. 5 = 2 Another way to describe this score is that it is 2 standard deviations above the mean. Z = (observation - mean) / SD. In the following frequency distribution which has 17 scores, the median would be the 9th score from the bottom which would be a 2 since both the 9th and 10th scores are 2. Now we would like to know how well George performed compared to his peers. Please enter the necessary parameter values, and then click 'Calculate'. z=2 b) A score that is 10 points below the mean. 2) However, a Standard Score will follow a normal distribution, also known as bell curve or Gaussian distribution. (Negative because it is below the mean. Wikipedia has good articles on statistics. To calculate the z-score you subtract the mean from and individual raw score (where your data point sits on the y axis) then dividing the difference by the standard deviation. From the normal distribution, we calculate the cumulative distribution, and use it to calculate the adjusted rating corresponding to each raw rating. In calculating z-scores, we convert a normal distribution into the standard normal distribution—this process is called. Derived Scores Quiz. This calculator transform your score into a normal standard distribution, where the resulting score will belong to a distribution with mean of 0 and standard deviation of 1. The standard normal distribution or the unit normal distribution is a special normal curve made up of z-scores. In either case, you will be more easily able to convert a z score to a percentiles if you know some basics about normal distributions, like the 68 95 99. Normal Distribution. Z-score calculator, p-value from z-table, left tail, right tail, two tail, formulas, work with steps, step by step calculation, real world and practice problems to learn how to find standard score for any raw value of X in the normal distribution. Normal distribution (percentile) Calculator - High accuracy calculation Welcome, Guest. The standard deviation of any SND always = 1. In that case, the distribution of bar(X) mean approaches a normal distribution as as per central limit theorem; for large sample size. Percentiles are used to compare scores across a larger sample, such as a national college admissions test like the ACT and SAT. Finding a z score involves performing a two-part calculation using three figures. An easy to use table for converting standard scores to T scores, scaled, scores, and percentiles, with interpretations. A distribution with an asymmetric tail extending out to the right is referred to as “positively skewed” or “skewed to the right,” while a distribution with an asymmetric tail extending out to the left is referred to as “negatively skewed” or “skewed to the left. Confidence Intervals about p 30. _____ Looking at graphs One informal but useful way of checking the skewness of a distribution is to look at the d. 9750 in the normal table, and get the z-value (1. Just enter your raw score, population mean and standard deviation, and hit "Calculate Z". DIST function, you will calculate the z-scores ncessary to determine probabiilty. Due to the. *This is a score interpretation guide for computer-based Step 1, Step 2 CK and Step 3 examinations. Problem 1: Find the probability that your neighbor has a lower ranked card. The z-score is the number of standard deviations from the mean. Related SOL: AFDA. Note, however, that the areas to the left of the dashed line are the same. You only need to enter one of each grades if there are multiples of the same score. Suppose the mean score on the math SAT is 500 and the standard deviation is 100. If you want to calculate the z score based on the raw score, mean, and standard deviation, see Z Score Calculator. In this table are a bunch of z-scores and proportions for the Standard Normal Distribution (which is the z-score standarized Normal distribution). The sten scoring system is normally distributed and then divided into ten parts by letting 0. The standard normal distribution can also be useful for computing percentiles. # The proportion of raw scores that fall above 90 is: 1-pnorm(90,mu,sigma) [1] 0. Verbal reasoning section and Quantitative Reasoning section are different scales, if we want to compare the raw scores, her percentile scores is more appropriate when comparing her performance to others. Calculate new X values for raw scores of X = 64 and X = 43 o What proportion of a normal distribution corresponds to z-scores within 1. Convert the standard score Z to a raw score X using the inverse formula: X Z For p Z z 0. when the distribution is normal can we use Z scores to calculate percentiles. Normal Distribution. As a result, a z score represents the number of standard deviations that a score is above or below the mean. Background. The z-scores are also listed on this normal distribution to show how the actual measurements of height correspond to the z-scores, since the z-scores are simple arithmetic transformations of the actual measurements. Normal distribution is often a good approximation to the results of chance outcomes. The points on a standard normal distribution, which is a bell curve that peaks at zero and has a standard deviation of one, correspond to z scores. converting T-scores to percentiles, WITHOUT a table? person's raw score = 600 don't you integrate the normal distribution curve from 0 to your number of. z-score = (x - m) / s x is the raw score. Asymptotic (Wald) method based on a normal approximation, Binomial (Clopper-Pearson) 'exact' method based on the beta distribution, 'Wilson' Score interval, 'Agresti-Coull' (adjusted Wald) interval and 'Jeffreys' interval. This simple calculator allows you to calculate a standardized z-score for any raw value of X. All the best and keep on revising!. Once you assume that your data can be represented by a Normal Curve, you can now use the proportions of that curve to tell you information about a raw scores relative to the curve. 5% of the scores are above +1. , but not 603. For instance: You can calculate the proportion (or percentage) of raw scores that falls above or below a specific raw score. To do this, we refer back to the standard normal distribution table. Normal Curve Distribution of IQ Scores See more. Finding z-score for a percentile. Stanine scores are used in education to compare student performance over a normal distribution. Nancy is a sixth-grade student who scores 81. 94 in the middle of the normal distribution curve. The raw score computed is the actual score, or value, obtained. In calculating z-scores, we convert a normal distribution into the standard normal distribution—this process is called. Normal Distribution & Z-scores This video shows how to calculate "inside areas" and "areas in the extreme" in a normal distribution using Z-scores. Use this graph to calculate z-scores and to see the corresponding probabilities. Z-Scores and the Normal Distribution. The mean of the sampling distribution (𝜇𝑋 ) always equals the mean of the raw score distribution from which we sampled (𝜇𝑋) 3. Standard Score. The 3 Characteristics of Scaled Score vs Standard Score: 1) A Standard Score and a Scaled Score are both scores that we obtain from the transformation of another score (normally raw scores). find the area under the standard normal curve from the mean to raw score 122. Enter the mean, standard deviation and select whether left tailed or right tailed or two tailed in this normal distribution curve generator to get the result. Thus the z-score is 1. 7, what is your percentile score? Solution: To figure out what percentile this score is in, we need to find the probability of getting a lower score, and then multiply by 100. The raw score allows students to find their letter grades on curved tests. Statistics 101 (Mine C¸etinkaya-Rundel) L6: Normal distribution February 2, 2012 10 / 24 Normal distribution Standardizing with Z scores Percentiles Percentile is the percentage of observations that fall below a given data point. If conversely what you have is a z-score, you can use our z-score to percentile calculator. Shade in the relevant area (probability), and label the mean, standard deviation, lower bound, and upper bound that you are given or trying to find. There is one difference, though. That is, if the sampling distribution were shaped as a normal distribution, 2. Raw Data Robust Data Normal Q Example: 135 Labs run % Calcium Analysis % Calcium quantiles(y axis) are plotted against Normal scores (x axis) for the ordered data (green). Further, a positive Z score implies a score that is higher than the mean, while a negative Z score implies a score less than the mean. This calculator will compute a Z-score (i. We can get a reasonable prior distribution by taking the distribution of scaled scores, mapping them back to raw scores, and converting raw scores to percentages. We can do this by taking the cumulative * proportions of raw scores as probabilities, finding their * corresponding normal deviates, and converting them to normalized * scores with a desired mean and standard deviation. Standard normal failure distribution. Normal distribution are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Just follow the below 2 steps to create statistical distribution / frequency of any set of values using excel. If you want to calculate the z score based on the raw score, mean, and standard deviation, see Z Score Calculator. It is required to calculate the Z-score for an observation. ) Lay people are sometimes uncomfortable with z-scores for a couple reasons. To find the mean and higher moments of the lognormal distribution, we once again rely on basic information about normal distribution. Areas are randomly generated so each student has a unique problem. , symmetrical bell-shaped figure used to represent the distribution of many physical and psychological characteristics , The maximum height of a normal curve corresponds to the _____ of a normal distribution. This is called estimating the area under the curve. The TI-89 Titanium’s Stats/List Editor contains a simple menu where you can look up a Z Score in seconds. 3 independent groups, population standard deviations known: The mean lasting time of 2 com-peting ﬂoor waxes is to be compared. The calculator will then automatically calculate the area between the 2 z scores, according to the formula z2-z1. That means that it corresponds to probability. In accounting, you might want to. Approximately what percentage of the cases. We can standardized the values (raw scores) of a normal distribution by converting them into z-scores. Entering the appropriate values in the normal curve area program for a score of 29 in the Normal Curve Area program would yield a percentile rank based on the normal curve of 24% as demonstrated below. Scores for Linear Rank and One-Way ANOVA Tests For each score type that you specify, PROC NPAR1WAY computes a one-way ANOVA statistic and also a linear rank statistic for two-sample data. The Z-Score Formula The formula for calculating the z-score of any particular data set is z = (x - μ) / σ where μ is the mean of a population and σ is the standard deviation of a population. f of the standard normal distribution table", finds a probability valuse as close to 0. Find the z-scores corresponding to each of the following values: a) A score that is 20 points above the mean. By its very definition, it is not. Normal Distribution & Z-scores This video shows how to calculate "inside areas" and "areas in the extreme" in a normal distribution using Z-scores. The standard normal distribution is a normal distribution with a standard deviation on 1 and a mean of 0. Calculate the z-score for each student. …It's called the Standard Normal Distribution. When you have a bell shaped curve, none of the 5 Ms or one P are unduly influencing the process. That is, you are given the percentage or statistical probability of being at or below a certain x-value, and you have to find the x-value that corresponds to it. 5? When in doubt draw a picture: Find the z score associated with. The formula below is used. To calculate the z-score you subtract the mean from and individual raw score (where your data point sits on the y axis) then dividing the difference by the standard deviation. 736σ To convert these sigma values into a percentage you can look them up in a standard z-table, use the Excel formula =NORMSDIST(1. Testing of hypothesis. For instance: You can calculate the proportion (or percentage) of raw scores that falls above or below a specific raw score. ALEKS: Explained and unexplained variation and the least-squares regression equation - Duration: 11:34. There are many data sets that follow a normal distribution. Find the z-score for the given raw score, mean, and standard deviation. Jim’s score is 24 21 5 = 0:6 standard deviations above the. This probability distribution is particularly useful as it can represent any normal distribution, whatever its mean and standard deviation. Please enter the necessary parameter values, and then click 'Calculate'. First, we can express any value in a distribution as a Z-score, a number that indicates how many standard deviations from the mean a score lies. This handy tool. How standardized language and speech testing works. Processing. We want to compute P(X < 30). This is a common need for a wide variety of data. A normal distribution with mean μ = 0, and standard deviation σ = 1 is called a standard normal distribution. Finally, calculate the z-score using the formula: (student result - Mean) / Standard Deviation. Twenty ﬂoors are randomly assigned to test each wax. You may also change the portion of the normal distribution selected: Cumulative--from minus. This will give you roughly half positive and half negative scores (called deviation scores). Just as a reminder - double check your numbers and always calculate your z score twice!. Enter answer as a positive value rounded to nearest hundredth (two places after decimal). 054 standard deviations above the mean. Jake needs to score in the top 10% in order to earn a physical fitness certificate. Additional eligibility requirements included that all participants were community dwelling, had a baseline MMSE score ≥ 25, normal performance on cognitive tests (within 1. Z-Scores and the Normal Distribution. Find the z-score for the given raw score, mean, and standard deviation. Background. For example, if you scored in the 85th percentile, you scored higher than 85 percent of test takers. The standard normal distribution (illustrated in the graph below) is a normal distribution with a mean of 0 and a standard deviation of 1.